Question

Prove $\sum _{k=2}^{n} k(k-1) {n \choose k}=n(n-1)2^{n-2}$

score 335 · Answer 1 · 2016-04-19 17:57:34

335

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Prove $\sum _{k=2}^{n} k(k-1) {n \choose k}=n(n-1)2^{n-2}$

Published on 19 Apr 2016 - 17:57

score 143 · Answer 2 · 2016-04-22 20:23:06

143

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Is it true for $n > 2$ then there always exists a prime $\le n$ that does not divide $n$?

Published on 22 Apr 2016 - 20:23

score 127 · Answer 3 · 2016-04-23 12:31:58

127

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The number of zeros in the expansion of $n!$ in base $12$

Published on 23 Apr 2016 - 12:31

score 157 · Answer 4 · 2016-04-26 16:54:59

157

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finding the smallest number $n$ such that $n!=n(n+1)(n+2)(n+3)$

Published on 26 Apr 2016 - 16:54

score 211 · Answer 5 · 2016-04-29 20:22:40

211

Views

Proof by strong induction combinatorics problem: $1(1!) + 2(2!) + 3(3!) + \dots + n(n!) = (n+1)! - 1$

Published on 29 Apr 2016 - 20:22

score 69 · Answer 6 · 2016-04-30 14:32:27

69

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solve for $\lim_{n \to \infty} \frac{6(n+1)(6n-1)!}{(6n+5)!}$

Published on 30 Apr 2016 - 14:32

score 104 · Answer 7 · 2016-05-01 10:46:10

104

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Maxima and minima of $f(x)=\binom{16-x}{2x-1}+\binom{20-3x}{4x-5}$.

Published on 01 May 2016 - 10:46

score 128 · Answer 8 · 2016-05-01 15:31:08

128

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Estimating $n!$ as $e \left(\frac ne \right)^n \le n! \le ne \left(\frac ne \right)^n$

Published on 01 May 2016 - 15:31

score 105 · Answer 9 · 2016-05-01 23:05:39

105

Views

Help solving the inequality $2^n \leq (n+1)!$, n is integer

Published on 01 May 2016 - 23:05

score 354 · Answer 10 · 2016-05-03 20:39:25

354

Views

solve for $\lim_{n \to \infty} \frac{(3n)!(1/27)^n}{(n!)^3}$

Published on 03 May 2016 - 20:39

score 323 · Answer 11 · 2016-05-04 17:14:41

323

Views

For integer $n>2$, $(n!)^2 > n^n$

Published on 04 May 2016 - 17:14

score 87 · Answer 12 · 2016-05-05 05:35:07

87

Views

Demonstrating that 1! is = 1

Published on 05 May 2016 - 5:35

score 1.9k · Answer 13 · 2016-05-05 22:36:11

1.9k

Views

Trying to Express A Factorial As A Polynomial

Published on 05 May 2016 - 22:36

score 2.9k · Answer 14 · 2016-05-06 04:57:14

2.9k

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Suppose a coin in tossed $12$ times and there are $3$ heads and $9$ tails. How many sequences...

Published on 06 May 2016 - 4:57

score 101 · Answer 15 · 2016-05-06 05:44:29

101

Views

Prove using factorials that ${n\choose k}+2{n\choose k+1}+{n\choose k+2}={n+2\choose k+2}$

Published on 06 May 2016 - 5:44

List Question

Prove $\sum _{k=2}^{n} k(k-1) {n \choose k}=n(n-1)2^{n-2}$

Is it true for $n > 2$ then there always exists a prime $\le n$ that does not divide $n$?

The number of zeros in the expansion of $n!$ in base $12$

finding the smallest number $n$ such that $n!=n(n+1)(n+2)(n+3)$

Proof by strong induction combinatorics problem: $1(1!) + 2(2!) + 3(3!) + \dots + n(n!) = (n+1)! - 1$

solve for $\lim_{n \to \infty} \frac{6(n+1)(6n-1)!}{(6n+5)!}$

Maxima and minima of $f(x)=\binom{16-x}{2x-1}+\binom{20-3x}{4x-5}$.

Estimating $n!$ as $e \left(\frac ne \right)^n \le n! \le ne \left(\frac ne \right)^n$

Help solving the inequality $2^n \leq (n+1)!$, n is integer

solve for $\lim_{n \to \infty} \frac{(3n)!(1/27)^n}{(n!)^3}$

For integer $n>2$, $(n!)^2 > n^n$

Demonstrating that 1! is = 1

Trying to Express A Factorial As A Polynomial

Suppose a coin in tossed $12$ times and there are $3$ heads and $9$ tails. How many sequences...

Prove using factorials that ${n\choose k}+2{n\choose k+1}+{n\choose k+2}={n+2\choose k+2}$

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